5.112 Principles Of Chemical Science Worksheet With Answers - Problem Set #4 Solutions - 2011 Page 7
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16Problem set #4 solutions for 5.112, Fall 2011
Page 7 of 16
(
)
(
)
-1
-1
3 8.315 J mol
K
2200 K
=
= 646.53 m s
-1
v
(
)
rms
−3
-1
131.29 x 10
kg mol
= 6.5 x 10
2
-1
v
m s
(correct sig figs)
rms
2
-1
escape velocity
6.46 x 10
m s
(
)
=
Ratio of
100
3
-1
root-mean square velocity
11.2 x 10
m s
= 0.05773
= 0.058 (correct sig figs)
The ratio of the escape velocity to the root mean square speeds are 0.33 (for He), 0.10 (for Ar) and
0.058 (for Xe). Helium is much more likely to escape than the heavier gases so this means that it
will not be found at high abundance in our atmosphere.
Question 11 (out of 2 points)
A confined gas of Ar is heated so that its pressure is tripled. If the volume remains the same,
how much kinetic energy does the gas gain or lose?
Think about the ideal gas law, PV=nRT. If the pressure is doubled, volume stays the same, we
can determine how the temperature has changed:
P
V
P
V
1
1
2
2
=
T
T
1
2
= V
know that P
= 3P
and
V
2
1
1
2
simplifying the relationship:
P
3P
1
1
=
= 3T
therefore : T
2
1
T
T
1
2
3
So, the temperature has tripled. Because E =
RT , the gas triples its kinetic energy
2
Question 12 (out of 4 points: 1 for part (a), 3 for part (b))
Six Rb atoms, with speeds of 1.2, 1.4, 1.6, 1.6, 2.0 and 2.5 m/s, are trapped in a laser trap.
(a) Determine the most probable speed for this distribution of six atoms.
-1
The most probable speed is 1.6 m s
. There are two atoms with that speed.
(b) Calculate the root mean square speed for this distribution of six atoms.
The root mean square speed is:
1
(
)
(
)
(
)
(
)
(
)
⎛
⎞
2
2
2
2
2
( )
1
2
-1
-1
-1
-1
-1
+ 1.4 m s
+ 2 1.6 m s
+ 2.0 m s
+ 2.5 m s
1.2 m s
⎜
⎟
2
2
=
v
⎜
⎟
6
⎜
⎟
⎝
⎠
1
⎛
⎞
2
-2
2
-2
2
-2
2
-2
2
-2
+ 2.074 m
+ 5.12 m
+ 4.0 m
+ 6.25 m
2
1.44 m
s
s
s
s
s
=
⎜
⎟
⎝
⎠
6
1
⎛
⎞
2
-2
2
18.77 m
s
-1
-1
=
= 1.7687 m s
= 1.8 m s
⎜
⎟
⎝
⎠
6
-1
The root mean square speed for the six Rb atoms is 1.8 m s
.
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